1. Among 157 Jamaican men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis of these data, we may conclude that the mean systolic blood pressure for a population of Jamaican is greater than 140. Use =0.01 2. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Symptoms of a latex allergy include conjunctivitis, hand eczema, nasal congestion, a skin rash, and shortness of breath. Each in a sample of 46 hospital employees who were diagnosed with latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are xx = 19.3 and s = 11.9. a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy. b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy. c. Give a practical interpretation of the interval you found in part b. d. Give the conditions required for the interval in part b to be valid. 3. A cover shoe manufacturer collected data regarding cover shoe sizes for medical practitioners and found that the distribution of sizes exactly fits a normal curve. If the mean shoe size is 11 and the standard deviation is 1.5. (a)What is the probability of randomly selecting a man with a shoe size smaller than 9.5? (b)If I surveyed 40 men, how many would be expected to wear smaller than 9.5